Volume 3, Issue 1
Stabilized Crank-Nicolson/Adams-Bashforth Schemes for Phase Field Models

Xinlong Feng, Tao Tang & Jiang Yang

East Asian J. Appl. Math., 3 (2013), pp. 59-80.

Published online: 2018-02

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  • Abstract

In this paper, stabilized Crank-Nicolson/Adams-Bashforth schemes are presented for the Allen-Cahn and Cahn-Hilliard equations. It is shown that the proposed time discretization schemes are either unconditionally energy stable, or conditionally energy stable under some reasonable stability conditions. Optimal error estimates for the semi-discrete schemes and fully-discrete schemes will be derived. Numerical experiments are carried out to demonstrate the theoretical results.

  • Keywords

Allen-Cahn equation Cahn-Hilliard equation Crank-Nicolson scheme Adams-Bashforth scheme implicit-explicit method error estimates

  • AMS Subject Headings

35L70 65N30 76D06

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COPYRIGHT: © Global Science Press

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@Article{EAJAM-3-59, author = {Xinlong Feng, Tao Tang and Jiang Yang}, title = {Stabilized Crank-Nicolson/Adams-Bashforth Schemes for Phase Field Models}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {3}, number = {1}, pages = {59--80}, abstract = {

In this paper, stabilized Crank-Nicolson/Adams-Bashforth schemes are presented for the Allen-Cahn and Cahn-Hilliard equations. It is shown that the proposed time discretization schemes are either unconditionally energy stable, or conditionally energy stable under some reasonable stability conditions. Optimal error estimates for the semi-discrete schemes and fully-discrete schemes will be derived. Numerical experiments are carried out to demonstrate the theoretical results.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.200113.220213a}, url = {http://global-sci.org/intro/article_detail/eajam/10847.html} }
TY - JOUR T1 - Stabilized Crank-Nicolson/Adams-Bashforth Schemes for Phase Field Models AU - Xinlong Feng, Tao Tang & Jiang Yang JO - East Asian Journal on Applied Mathematics VL - 1 SP - 59 EP - 80 PY - 2018 DA - 2018/02 SN - 3 DO - http://dor.org/10.4208/eajam.200113.220213a UR - https://global-sci.org/intro/article_detail/eajam/10847.html KW - Allen-Cahn equation KW - Cahn-Hilliard equation KW - Crank-Nicolson scheme KW - Adams-Bashforth scheme KW - implicit-explicit method KW - error estimates AB -

In this paper, stabilized Crank-Nicolson/Adams-Bashforth schemes are presented for the Allen-Cahn and Cahn-Hilliard equations. It is shown that the proposed time discretization schemes are either unconditionally energy stable, or conditionally energy stable under some reasonable stability conditions. Optimal error estimates for the semi-discrete schemes and fully-discrete schemes will be derived. Numerical experiments are carried out to demonstrate the theoretical results.

Xinlong Feng, Tao Tang & Jiang Yang. (1970). Stabilized Crank-Nicolson/Adams-Bashforth Schemes for Phase Field Models. East Asian Journal on Applied Mathematics. 3 (1). 59-80. doi:10.4208/eajam.200113.220213a
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